A New Approach to Evaluate the Performance of Value-at-risk Estimators, Using Genetic Algorithms

Value at Risk (VaR) is the maximum loss which could be incurred within a given time horizon, except for a small percentage, that its application has sharply increased after the 90s. Parallel to the increase in usage of value-at-risk in risk management areas, validation of VaR measures has gain great importance. In prevalent back testing approaches, returns which are yielded from VaR estimators are not regarded as a criterion. It's may not be desirable for the investors who emphasize on return more than the risk. What distinguishes this study from other researches in the field of back testing VaR estimation models is the simultaneous consideration of actual return and loss(CVaR) which were yielded from VaR estimators as criteria of risk and return that are the primary basis for financial studies. On the other hand, due to relativeness of risk and return in terms of investors, we considered the weight of these two indexes as fuzzy. In this paper, we constitute and optimize our risky portfolio with safety-first investor's rule. We need to estimate quantile of risky portfolio's return in objective function of safety-first investor's rule to optimize the portfolio. VaR estimators were used to calculate it. On the other hand, given the non- convexity of VaR function and also other reasons, we applied one of the most popular meta-heuristic models namely genetic algorithms for optimization. Our findings show that GEV and HS models are more conservative than parametric models (t-student and normal) and also have better performance in portfolio optimization. The empirical findings also indicate that safety-first investor will choose significantly different amounts of borrowing. Thus, the scale of the risky portfolio and the amount borrowed is diverse across methods. There is another interesting finding. Despite the computational simplicity of historical simulation method, it has shown the best performance of all.